# A memory-free spatial additive mixed modeling for big spatial data

@article{Murakami2019AMS, title={A memory-free spatial additive mixed modeling for big spatial data}, author={Daisuke Murakami and Daniel A. Griffith}, journal={Japanese Journal of Statistics and Data Science}, year={2019}, volume={3}, pages={215-241} }

This study develops a spatial additive mixed modeling (AMM) approach estimating spatial and non-spatial effects from large samples, such as millions of observations. Although fast AMM approaches are already well established, they are restrictive in that they assume a known spatial dependence structure. To overcome this limitation, this study develops a fast AMM with the estimation of spatial structure in residuals and regression coefficients together with non-spatial effects. We rely on a Moranβ¦Β

## 10 Citations

Balancing Spatial and NonβSpatial Variation in Varying Coefficient Modeling: A Remedy for Spurious Correlation

- MathematicsGeographical Analysis
- 2021

This study discusses the importance of balancing spatial and non-spatial variation in spatial regression modeling. Unlike spatially varying coefficients (SVC) modeling, which is popular in spatialβ¦

Scalable GWR: A Linear-Time Algorithm for Large-Scale Geographically Weighted Regression with Polynomial Kernels

- Computer Science, Mathematics
- 2019

The key improvement is the calibration of the model through a precompression of the matrices and vectors whose size depends on the sample size, prior to the leave-one-out cross-validation, which is the heaviest computational step in conventional GWR.

spmoran: An R package for Moran's eigenvector-based spatial regression analysis

- Computer Science
- 2017

The objective of this study is illustrating how to use "spmoran," which is an R package for Moran's eigenvector-based spatial regression analysis, which applies ESF and RE-ESF models for a land price analysis.

The GWR route map: a guide to the informed application of Geographically Weighted Regression

- Computer Science, Mathematics
- 2020

A route map is described to inform the choice of whether to use a GWR model or not, and if so which of three core variants to apply: a standard GWR, a mixed GWR or a multiscale GWR (MS-GWR).

Does financial deepening drive spatial heterogeneity of PM2.5 concentrations in China? New evidence from an eigenvector spatial filtering approach

- Economics
- 2021

Abstract To provide policymakers with a different perspective on reducing PM2.5 concentrations, this paper not only identifies the economic driving factors of PM2.5 concentrations in China but alsoβ¦

Spatial heterogeneity and economic driving factors of SO2 emissions in China: Evidence from an eigenvector based spatial filtering approach

- Environmental Science
- 2021

Sulfur dioxide (SO2) emissions have been a great challenge in China over the last few decades due to their serious impact on the environment and human health. In this paper, a random effectβ¦

Investigating high-speed rail construction's support to county level regional development in China: An eigenvector based spatial filtering panel data analysis

- Geography
- 2020

The construction of high-speed rail in China was initially a direct response to the increasing demand of up-to-date infrastructure. It is commonly understood that the construction of HSR hasβ¦

Spatial regression modeling using the spmoran package: Boston housing price data examples

- Mathematics
- 2017

An approximate Gaussian process (GP or kriging model), which is interpretable in terms of the Moran coefficient (MC), is used for modeling the spatial process. The approximate GP is defined by aβ¦

Compositionally-warped additive mixed modeling for a wide variety of non-Gaussian spatial data

- Computer Science, Mathematics
- 2021

A general framework for fast and flexible non-Gaussian regression, especially for spatial/spatiotemporal modeling is developed and the developed model, termed the compositionally-warped additive mixed model (CAMM), provides intuitively reasonable coefficient estimates and outperforms AMM in terms of prediction accuracy.

Scalable Model Selection for Spatial Additive Mixed Modeling: Application to Crime Analysis

- Mathematics, Computer ScienceISPRS Int. J. Geo Inf.
- 2020

A fast and practical model-selection approach for spatial regression models, focusing on the selection of coefficient types that include constant, spatially varying, and non-spatially varying coefficients, that is useful not only for selecting factors influencing crime risk but also for predicting crime events.

## References

SHOWING 1-10 OF 80 REFERENCES

Spatially varying coefficient modeling for large datasets: Eliminating N from spatial regressions

- MathematicsSpatial Statistics
- 2019

Abstract While spatially varying coefficient (SVC) modeling is popular in applied science, its computational burden is substantial. This is especially true if a multiscale property of SVC isβ¦

Limitations on low rank approximations for covariance matrices of spatial data

- Mathematics
- 2014

Abstract Evaluating the likelihood function for Gaussian models when a spatial process is observed irregularly is problematic for larger datasets due to constraints of memory and calculation. If theβ¦

A Case Study Competition Among Methods for Analyzing Large Spatial Data

- Medicine, Computer ScienceJournal of agricultural, biological, and environmental statistics
- 2019

This study provides an introductory overview of several methods for analyzing large spatial data and describes the results of a predictive competition among the described methods as implemented by different groups with strong expertise in the methodology.

Gaussian predictive process models for large spatial data sets.

- Mathematics, MedicineJournal of the Royal Statistical Society. Series B, Statistical methodology
- 2008

This work achieves the flexibility to accommodate non-stationary, non-Gaussian, possibly multivariate, possibly spatiotemporal processes in the context of large data sets in the form of a computational template encompassing these diverse settings.

Hierarchical Nearest-Neighbor Gaussian Process Models for Large Geostatistical Datasets

- Computer Science, MedicineJournal of the American Statistical Association
- 2016

A class of highly scalable nearest-neighbor Gaussian process (NNGP) models to provide fully model-based inference for large geostatistical datasets are developed and it is established that the NNGP is a well-defined spatial process providing legitimate finite-dimensional Gaussian densities with sparse precision matrices.

Generalized Additive Models for Gigadata: Modeling the U.K. Black Smoke Network Daily Data

- Computer Science
- 2017

Abstract We develop scalable methods for fitting penalized regression spline based generalized additive models with of the order of 104 coefficients to up to 108 data. Computational feasibility restsβ¦

Fixed rank kriging for very large spatial data sets

- Mathematics
- 2008

Spatial statistics for very large spatial data sets is challenging. The size of the data set, "n", causes problems in computing optimal spatial predictors such as kriging, since its computationalβ¦

A Multi-Resolution Approximation for Massive Spatial Datasets

- Mathematics, Computer Science
- 2015

A multi-resolution approximation (M-RA) of Gaussian processes observed at irregular locations in space is proposed, which can capture spatial structure from very fine to very large scales.

Dimension reduction and alleviation of confounding for spatial generalized linear mixed models

- Computer Science, Mathematics
- 2010

This work proposes a new parameterization of the spatial generalized linear mixed model that alleviates spatial confounding and speeds computation by greatly reducing the dimension of theatial random effects.

Penalized basis models for very large spatial datasets

- Computer Science, Mathematics
- 2019

Under a Gaussianity assumption, this work proposes a graphical model family for the stochastic coefficients by parameterizing the precision matrix and develops a flexible nonstationary spatial model that is adaptable to very large datasets.